Solve 2sqrt{5*125div2}

$$2 \sqrt{ 5 \times 125 \div 2 }$$

Evaluate

$$25\sqrt{2}\approx 35.355339059$$

Solution Steps

Multiply 5 and 125 to get 625.

$$2\sqrt{\frac{625}{2}}$$

Rewrite the square root of the division \sqrt{\frac{625}{2}} as the division of square roots \frac{\sqrt{625}}{\sqrt{2}}.

$$2\times \frac{\sqrt{625}}{\sqrt{2}}$$

Calculate the square root of 625 and get 25.

$$2\times \frac{25}{\sqrt{2}}$$

Rationalize the denominator of \frac{25}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$2\times \frac{25\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$2\times \frac{25\sqrt{2}}{2}$$

Cancel out 2 and 2.

$$25\sqrt{2}$$